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  • Under isothermal condition, the pressure of a gas is given by <img alt="\mathrm{P}=\mathrm{aV}^{-3}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BP%7D%3D%5Cmathrm%7BaV%7D%5

Under isothermal condition, the pressure of a gas is given by \mathrm{P}=\mathrm{aV}^{-3}, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to


 

Option: 1

\frac{\text{P}}{2}


Option: 2

\mathrm{2P}


Option: 3

\mathrm{P}


Option: 4

\mathrm{3P}


Answers (1)

best_answer

\begin{aligned} & \mathrm{P}=\mathrm{aV}^{-3} \\ & \frac{\mathrm{dP}}{\mathrm{dV}}=-3 \mathrm{aV}^{-4} \end{aligned}

\text { Bulk modulus, } \mathrm{B}=-\mathrm{V} \frac{\mathrm{dP}}{\mathrm{dV}}

\begin{aligned} & \mathrm{B}=-\mathrm{V}\left(\frac{-3 \mathrm{a}}{\mathrm{V}^4}\right) \\ & \mathrm{B}=3 \frac{\mathrm{a}}{\mathrm{V}^3}=3 \mathrm{P} \end{aligned}

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